The platooning of vehicles is a very important technique for enhancing the traffic capacity without additional road network and improving the traffic safety. In the platooning, vehicles travel in the row so as to keep the vehicle head distance short. The most important thing from the existing studies is to realize the stable platooning of vehicles. On the other hand, our research group focuses on the control of the platooning of vehicles in several use cases such as junction and intersection. In this paper, the control of the platooning of vehicles in the intersection or crossover point is studied. The simulation region is the intersection of two straight roads. Two groups of two vehicles travel on different roads and meet at the intersection. The velocity of the vehicles is controlled by the vehicle following model. The model parameters are first designed in the computer simulation. The validity of the velocity and the behavior control models are discussed in the experiment of LEGO Mindstorm. The results show that the model can control the vehicles in the platoons safely.